Induction Correlation and Causation Deduction vs Induction

Induction, Correlation, and Causation

Deduction vs. Induction (1) All ravens are black. (2) Therefore, the raven hiding behind that branch of the tree must be black. (1) A raven I saw yesterday was black. (2) Another raven I saw a couple of days ago was black. …… (3) Therefore, all ravens are black.

• A good non-deductive argument is an argument in which its premises support the conclusion but do not ensure it. • In other words, the true premises of a good non -deductive argument make the conclusion only likely to be true.

• Valid deductive arguments are truth-preserving. Good non-deductive arguments are not necessarily truth-preserving. • Deductive arguments are non-ampliative. Non-deductive arguments are ampliative.

Types of Non-deductive arguments • Induction – enumerative induction; statistical reasoning, probabilistic reasoning, general induction • Abduction (Explanatory Inference, Inference to the Best Explanation: IBE)

• A statement is particular if it is about a particular subject, time, place, etc. • A statement is general if it is about a collection of subjects, tendency, etc. • A general statement is either universal or statistical. Universal statements are statements with expressions like ‘all, ’ ‘every, ’ ‘none, ’ etc. Statistical statements apply to only some or most.

• Particular → General A raven I saw yesterday was black. Another raven I saw a couple of days ago was black. …… Therefore, all ravens are black.

• General (Statistical) → Particular Most adults can tolerate moderate amounts of sugar in their diets. Alvin is an adult. Therefore, Alvin can tolerate moderate amounts of sugar in his diet.

Universal vs. Statistical • Particular → General (Universal) A raven I saw yesterday was black. Another raven I saw a couple of days ago was black. …… Therefore, all ravens are black. • Particular → General (Statistical) x percent of P’s in the sample are Q’s Therefore, x percent of P’s in the population are Q’s.

Enumerative Induction • Type 1 (to a general law or principle): a 1, a 2, …, an are all Fs that are also Gs. Therefore, all Fs are Gs. • Type 2 (to a singular statement): a 1, a 2, …, an are all Fs that are also Gs. an+1 is an F. Therefore, an+1 is also a G.

Deductive vs. Statististical Reasoning (1) All adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, Alvin can tolerate moderate amounts of sugar in his diet. (1) Most adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, Alvin can tolerate moderate amounts of sugar in his diet. (1) 95% of adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, Alvin can tolerate moderate amounts of sugar in his diet.

Statistical vs. Probabilistic Reasoning (1) Most adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, Alvin can tolerate moderate amounts of sugar in his diet. (1) Most adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, Alvin can probably tolerate moderate amounts of sugar in his diet. (1) 95% of adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, the probability that Alvin can tolerate moderate amounts of sugar in his diet is 95%.

Probabilistic Reasoning (1) 95% of adults can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, the probability that Alvin can tolerate moderate amounts of sugar in his diet is 95%. (1) 95% of adults who have been tested can tolerate moderate amounts of sugar in their diets. (2) Alvin is an adult. (3) Therefore, the probability that Alvin can tolerate moderate amounts of sugar in his diet is 95%.

Bertrand Russell’s Inductivist Turkey The turkey found that, on his first morning at the turkey farm, that he was fed at 9 a. m. Being a good inductivist turkey he did not jump to conclusions. He waited until he collected a large number of observations that he was fed at 9 a. m. and made these observations under a wide range of circumstances, on Wednesdays, on Thursdays, on cold days, on warm days. Each day he added another observation statement to his list. Finally he was satisfied that he had collected a number of observation statements to inductively infer that “I am always fed at 9 a. m. ” However on the morning of Thanksgiving he was not fed but instead his throat cut.

Inductive generalizations that have turned out to be false • All swans are white. http: //en. wikipedia. org/wiki/Black_Swan • Mercury is the best remedy for syphilis. • Many scientific theories: Newtonian mechanics

Smoking causes lung cancer. http: //en. wikipedia. org/wiki/Tobacco_packaging_warning_messages

Hume’s Problem of Induction • Induction is never justified! • Induction cannot be justified inductively nor deductively.

Correlations • Two factors A and B are • There is a significant correlated with each correlation between other if the increase of going to hospital and A and the increase of B dying. go in tandem. • There is a significant correlation between the increase in the number of hours children watch TV and a decrease in the college admission test scores.

Causation A causal relation is more than a correlation. Unlike Correlation: • Causation is not symmetric. • Causation has a direction. • Examples You flip a switch, and then the light turns on. Your flipping a switch causes the light to turn on. You turn the key and the engine starts. Your turning the key causes the engine to start.

Are these causations? • Ice cream sales and the number of shark attacks on swimmers are correlated. • Skirt lengths and stock prices are highly correlated (as stock prices go up, skirt lengths get shorter). • The number of cavities in elementary school children and vocabulary size have a strong positive correlation.

• http: //news. bbc. co. uk/2/hi/health/2292143. stm

• From September through December of this year, Amalie had been very shy and selfconscious around her classmates, causing her to shun social interaction. In March, however, she began displaying noticeable confidence and sociability, which was also the month she began to participate in a very popular afterschool drama workshop. Clearly, the workshop has worked wonders for Amalie’s self-esteem.

• The majority of professional Canadian ice hockey players are born in the first few months of the calendar year. If you look at list of the best players you’ll see that most of them are born sometime in January through April — with the highest concentrations in the earliest months. Why is that?

• Gladwell argues that the answer is that youth hockey leagues determine eligibility by calendar year, so that children born in January play in the same league as those born in December 31. Since adolescents born earlier in the year tend to be more developmentally advanced than the others, they are often identified as better athletes. This leads to them being “bumped up” to the better leagues and in turn receiving extra coaching and a higher likelihood of being selected for elite hockey leagues.

Current movies, television programs, magazines, and video games are bringing about a moral degeneration in our country. They are filled with sexual and violent images, exposure to which leads viewers and readers to aggressive, violent, and morally corrupt sexual behaviors.

An episode of The Simpsons (Season 7, "Much Apu About Nothing") • Springfield had just spent millions of dollars creating a highly sophisticated "Bear Patrol" in response to the sighting of a single bear the week before. – – – – – Homer: Not a bear in sight. The "Bear Patrol" is working like a charm! Lisa: That's specious reasoning, Dad. Homer: [uncomprehendingly] Thanks, honey. Lisa: By your logic, I could claim that this rock keeps tigers away. Homer: Hmm. How does it work? Lisa: It doesn't work. (pause) It's just a stupid rock! Homer: Uh-huh. Lisa: But I don't see any tigers around, do you? Homer: (pause) Lisa, I want to buy your rock.

One prison inmate says to another: “Governor Schwarzenegger always seems to know when we’re having a good meal. He times his annual inspection visit here on the one day of the year that we have steak. ”

Facebook Users Get Worse Grades in College • http: //news. yahoo. com/s/livescience/20090413/sc_livescience/facebookusersgetworsegradesincollege/print

• Anthropologists studying a tribe in the South Seas found the islanders believed that having body lice promotes good health. It turns out that this was not just superstition. Almost every healthy person had some body lice, but many sick people did not. So, there was a clear positive correlation between having body lice and being healthy.

• A sick person’s body temperature is usually higher than normal, and lice do not like high temperature. Thus, lice start looking for cooler surroundings. That is, it is not that lice make you healthy, but that being sick causes you not to have lice.

• A careful study of college students came up with the conclusion that there is a positive correlation between having a low GPA and smoking cigarettes. Opponents of cigarette smoking concluded that smoking causes students to get lower grades.

First born child is smarter • http: //www. newscientist. com/article/dn 12102

Fraternal birth order and sexual orientation • http: //en. wikipedia. org/wiki/Fraternal_birth_order